What you have to remember here is the formulas for area and circumference of a circle.
The area of a circle is equal to the square of its radius times pi. The circumference of a circle is equal to the diameter times pi.
So, let's look at what happens if you double the radius of a circle -- say from 2 to 4.
The area will go from 12.56 to 50.24. This means that it has quadrupled. The reason for this is that you square the radius. So when you double the radius, the area goes up by 4 times because 2 squared is 4. The area will always go up by the square of how much the radius goes up.
By contrast, the circumference will only double -- from 12.56 to 25.12 because you do not square the radius (or diameter) -- you just multiply it by pi. So the circumference will go up by the same percent that the radius does.